Lecture PowerPoint
Physics for Scientists and
Engineers, 3rd edition
Fishbane
Gasiorowicz
Thornton
© 2005 Pearson Prentice Hall
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Chapter 1
Tooling Up
Main Points of Chapter 1
• Scientific method
• Scales from the very small to the very large
• Fundamental quantities, units, and unit
conversions
• Scientific notation
• Accuracy and significant figures
• Dimensional analysis
• Estimating
• Scalars and vectors
1-1 A Little Background
Scientific method: interplay between
observation and theory.
Observations can suggest new theories,
which lead to further observations, and so on.
1-1 A Little Background
Newton’s laws describe motions of everyday objects
extremely well.
Modifications are needed in the realm of the very
small – quantum mechanics – and the very large,
where we need general relativity.
Below we have an image showing single atoms and
a supernova remnant.
1-2 Fundamental Physical Quantities and
Their Units
Scientific notation: use powers of 10 for
numbers that are not between 1 and 10 (or,
often, between 0.1 and 100); exponents add if
multiplying and subtract if dividing:
1-2 Fundamental Physical Quantities and
Their Units
Fundamental physical quantities:
• Length
• Mass
• Time
All quantities that we use, until Chapter 21,
will be combinations of these three
quantities.
1-2 Fundamental Physical Quantities and
Their Units
The system of units we will use is the
Standard International (SI) system; the units
of the fundamental quantities are:
• Length – meter
• Mass – kilogram
• Time – second
1-2 Fundamental Physical Quantities and
Their Units
Standard references provide a universal calibration
of these units:
The meter is the speed of light (which is assigned a
fixed value) divided by one second.
1-2 Fundamental Physical Quantities and
Their Units
Standard references provide a universal calibration
of these units:
The second is 9,192,631,770 vibrations of 133Cs.
1-2 Fundamental Physical Quantities and
Their Units
Standard references provide a universal calibration
of these units:
The reference kilogram is a cylinder made of
platinum–iridium alloy and kept in the International
Bureau of Weights and Measures in France. A
search continues for a suitable atomic or natural
standard for mass.
1-2 Fundamental Physical Quantities and
Their Units
Other systems of units:
• cgs, which uses the centimeter, gram, and
second as basic units
• British, which uses the foot for length, the
second for time, and the pound for force or
weight – all of these units are now defined
relative to the SI system.
1-2 Fundamental Physical Quantities and
Their Units
Unit prefixes for powers of 10, used in the SI
system:
1-2 Fundamental Physical Quantities and
Their Units
Units and unit conversions
Derived units are those which are
combinations of the fundamental units. Some
of these are given their own names, and
others are not.
Velocity, m/s, does not have a special name,
but power, kg-m2/s2 does: the watt.
1-2 Fundamental Physical Quantities and
Their Units
Units and unit conversions
Quantities can be converted from the SI to the
cgs and British systems using conversion
constants.
1-3 Accuracy and Significant Figures
Uncertainty in measurement:
Almost no measurement can be done with
perfect accuracy – there are possible
variations that are below the limit of
detection.
1-3 Accuracy and Significant Figures
Uncertainty in measurement:
Measurements are often quoted with a
central value and an uncertainty, indicating
how accurate the measurement is.
If measurements are combined to form some
quantity, the effect of the uncertainty of each
needs to be taken into account.
1-3 Accuracy and Significant Figures
The number of significant figures represents the
accuracy with which a number is known.
Terminal zeroes after a decimal point are
significant figures:
2.0 is between 1.95 and 2.05, whereas 2.00 is
between 1.995 and 2.005.
1-3 Accuracy and Significant Figures
The number of significant figures represents the
accuracy with which a number is known.
Trailing zeroes with no decimal point are not
significant:
1200 is between 1150 and 1250, whereas 1200. is
between 1199.5 and 1200.5.
1-3 Accuracy and Significant Figures
If numbers are written in scientific notation, it
is clear how many significant figures there are:
6 × 1024 has one
6.1 × 1024 has two
6.14 × 1024 has three
…and so on.
Calculators typically show many more digits
than are significant. It is important to know
which are accurate and which are meaningless.
1-4 Dimensional Analysis
All the quantities we will deal with through
Chapter 20 are combinations of mass M,
length L, and time T.
1-4 Dimensional Analysis
The dimension of a quantity is the particular
combination that characterizes it (the brackets
indicate that we are talking about
dimensions):
[v] = [L]/[T]
Note that we are not specifying units here –
velocity could be measured in meters per
second, miles per hour, inches per year, or
whatever.
1-4 Dimensional Analysis
If two quantities are equated (on two
sides of an equation, for example), they
must have the same dimensions – you
can equate a velocity to a velocity, but not
to a length. Quantities that are added and
subtracted must also have the same
dimensions.
1-4 Dimensional Analysis
This provides an excellent check for
calculations! If separate quantities that
are to be added, subtracted, or equated
don’t have the same dimensions,
something is wrong somewhere.
1-5 Estimates – How a Little Reasoning
Goes a Long Way
Estimates are very helpful in understanding
what the solution to a particular problem
might be.
Generally an order of magnitude is enough –
is it 10, 100, or 1000?
Final quantity is only as accurate as the least
well estimated quantity in it
1-6 Scalars and Vectors
Scalar: ordinary algebraic quantity, such as mass
or temperature
Vector: Quantity that needs both magnitude and
direction for full description, such as velocity or
tension (in a rope)
Displacement vector: points from an object’s initial
position to its final one
1-6 Scalars and Vectors
Addition and subtraction of vectors
Adding vectors: Place vectors so the tail of the
second starts at the head of the first, and so on.
Vector sum points from tail of first to head of last.
1-6 Scalars and Vectors
Subtracting vectors: The negative of a
vector is the same magnitude as the
original, and points in the opposite
direction. Draw the vector appropriately
and proceed as for addition.
1-6 Scalars and Vectors
Scalar multiplication of
vector: Vector is still in
same direction (or opposite,
if multiplication factor is
negative); magnitude is
scaled by multiplication
factor.
1-6 Scalars and Vectors
Unit vector: has direction
and unit magnitude.
Vector can then be written:
1-6 Scalars and Vectors
Components: Can regard any vector not
lying along the x- or y-axis as being the
sum of two vectors, one along x and the
other along y.
1-6 Scalars and Vectors
Vector can then be described by x and y
components, or by a length and an angle:
1-6 Scalars and Vectors
The relative orientation for x-, y-, and z-axes
can be found using a right-hand rule:
Summary of Chapter 1
• Fundamental quantities are length, mass, and time
• Scientific notation is much easier to read than
strings of zeroes
• Derived units can be expressed in terms of
fundamental units
• Quantities to be added, subtracted, or equated
must have the same dimensions
• Physical quantities can be measured only to a
certain accuracy; this accuracy can be indicated by
the number of significant figures
Summary of Chapter 1, cont.
• Estimation is useful in solving problems;
often an order of magnitude is enough
• Vectors have both magnitude and direction
• Vectors can be added, subtracted, and
multiplied by scalars